We used a matrix notation
describing the string products as a diagonal matrix [1]}:
\(B^{(p,\bar{p})}_{p+r+1,\bar{p}+\bar{r}+1}\mid ^{(2r,2\bar{r})}\ =\ \delta _{p+r,\bar{p}+\bar{r}}B^{(p,\bar{p})}_{p+r+1}\mid ^{(2r,2\bar{r})}\,.\) 
